Solve for $x$, ignoring any extraneous solutions: $\dfrac{x^2}{x - 4} = \dfrac{16}{x - 4}$
Answer: Multiply both sides by $x - 4$ $ \dfrac{x^2}{x - 4} (x - 4) = \dfrac{16}{x - 4} (x - 4)$ $ x^2 = 16$ Subtract $16$ from both sides: $ x^2 - (16) = 16 - (16)$ $ x^2 - 16 = 0$ Factor the expression: $ (x - 4)(x + 4) = 0$ Therefore $x = 4$ or $x = -4$ However, the original expression is undefined when $x = 4$. Therefore, the only solution is $x = -4$.